NEW YORK — Food and Drug Administration inspectors are heading for farms in Florida and Mexico, as new clues emerge to the possible source of salmonella-tainted tomatoes that have now sickened 552 people.

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The FDA wouldn’t say where in Florida and Mexico the hunt is centering. But officials stressed the clues don’t mean that a particular farm will turn out to be the culprit.

Investigators will pay special attention to big packing houses or distribution warehouses that enough tomatoes from those farms may have traveled through to account for what appears to be the nation’s largest-ever salmonella outbreak from tomatoes.

Most of this newest influx of cases were people who got sick weeks ago but hadn’t been counted yet. Some states began doing a better job of checking for salmonella as the outbreak has dragged on, while part of the surge comes from test results that had been backlogged in jammed laboratories. Earlier today, six new illnesses connected to tainted tomatoes were confirmed in New York City.

What hasn’t changed is that the earliest known victim got sick on April 10, and the latest on June 5.

But New Hampshire and Pennsylvania reported their first cases, bringing to 30 the number of states — plus Washington, D.C. — that have reported sick residents, although some may have been infected while traveling. At least 48 people have been hospitalized.

It might be impossible to trace the ultimate source of the tainted tomatoes, the Food and Drug Administration’s food safety chief warned Wednesday.

“I know there is a great deal of frustration” that the mystery hasn’t been solved, said Dr. David Acheson, the FDA’s associate commissioner for foods. “We’re continuing to work flat-out.”

But tomatoes are among the hardest foods to trace in an outbreak, because people seldom have any left by the time they get sick and they’re sold without tags to help trace their suppliers.

The FDA has said that parts of Mexico and Florida are the most likely sources of the contamination because they were supplying most of the nation’s tomatoes when the outbreak began. But Acheson said he was “trying to inject a note of realism” that the longer his probe lasts, the less likely he’ll find the actual farm.

“As every day passes, it gets just a little more tricky,” he said. “I’m still optimistic but I’m trying to be realistic.”

As part of the probe, the FDA has asked Mexican health authorities to check whether they have any cases of this exact strain of salmonella Saintpaul, the subtype involved.

The FDA continues to urge consumers nationwide to avoid raw red plum, red Roma or red round tomatoes unless they were grown in specific states or countries that FDA has cleared of suspicion. Check FDA’s Web site — http://www.fda.gov— for an updated list. Also safe are grape tomatoes, cherry tomatoes and tomatoes sold with the vine still attached.